A Short Explanation of Why We Have Leap Years and When They Will Occur

One Year is Approximately Equal to 365.24219878 Days (Give or Take)
The Egyptians called it 365 and left it at that. But their calendar got out
of step with the seasons, so that after around 750 years of this they were
celebrating The Fourth of July in the middle of the winter. But consider the
benefits: here in Boston, Massachusetts, there was all that extra room for
picnics and blankets at the Esplanade on the frozen Charles River!
The
Romans wised up and added the leap day every four years to get the 365.25 day
Julian year. Much better, but notice that this time the year is longer than it
ought to be. The small difference between this and the true length of the year
caused the seasons to creep through the calendar once again, only slower and in
the other direction. After about 23000 years of this, July Fourth would once
again fall in midwinter.
Fortunately things never reached that sad
state. By 1582 the calendar was about ten days out of whack, so Pope Gregory
XIII included the correction that's still in use today.
If the year is divisible by 100, it's not a leap year UNLESS it is also
divisible by 400.
More recently, proposals for fixes have gotten even better than that. One
suggested change is to add on "if the year is also divisible by 4000, it's not a
leap year."
Here's what it looks like:
Egyptian
Formula: 365 Year length: 365 Error: 0.24219878 Years to get 6
months out of whack: 754
Julian
Formula: 365 + 1/4 Year length: 365.25 Error: 0.0078122 Years to
get 6 months out of whack: 23,377
Gregorian
Formula: 365 + 1/4  1/100 + 1/400 Year length: 365.2425 Error:
0.00030122 Years to get 6 months out of whack:
606,272
Modern?
Formula: 365 + 1/4  1/100 + 1/400  1/4000 Year length:
365.24225 Error: 0.00005122 Years to get 6 months out of whack:
3,565,426
